Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-13T14:35:32.002Z Has data issue: false hasContentIssue false
  • English
  • Français

The flow of a compressible fluid with weak entropy changes

Published online by Cambridge University Press:  28 March 2006

Roy Gundersen
Roy Gundersen
Affiliation:
Department of Mathematics, Illinois Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

Perturbations of a given flow are considered, and the equations which govern the one-dimensional, non-steady flow of an inviscid, ideal compressible gas are linearized in the neighbourhood of this known solution, assumed isentropic, by a formal perturbation expansion. The perturbed flow is not assumed isentropic. Explicit solutions are obtained for a basic flow which is uniform or a centred simple wave and for an arbitrary simple wave if the perturbed flow is isentropic.

The perturbation of a uniform shock and perturbations in a shock tube lead to functional equations of a particular type, and a discussion of their solution is given.

A similar analysis is used to discuss the flow in a tube of slowly varying cross-section.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 6 , March 1958 , pp. 553 - 581
Copyright
© 1958 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chester, W. 1953 Quart. J. Mech. Appl. Math. 6, 440.
Chester, W. 1954 Phil. Mag. 45, 1293.
Germain, P. & Gundersen, R. 1955 C. R. Acad. Sci., Paris, 241, 925.
Gundersen, R. 1954 Brown University Report AF-1021/1.
Lighthill, M. J. 1948 Proc. Roy. Soc. A, 198, 454.